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Given the following coupled system of ODES Ý, = 988y,-1998y, Ý, = 1000y,-2000y- with y: (0)= 1, y:(0)=2 a) Solve the system using Explicit Euler with h= 0.00001, 0.001 and 0.01 for 0x0.5. b) Solve the system using Implicit Euler with h=0.00001, 0.001 and 0.01 for 0sxs0.5. c) Plot the solutions (y vs. x) and (y vs. x) in a and b on the same graph and make your comments on the behavior of the system, accuracy and stability.

Given the following coupled system of ODES Ý, = 988y,-1998y, Ý, = 1000y,-2000y- with y: (0)= 1, y:(0)=2 a) Solve the system using Explicit Euler with h= 0.00001, 0.001 and 0.01 for 0x0.5. b) Solve the system using Implicit Euler with h=0.00001, 0.001 and 0.01 for 0sxs0.5. c) Plot the solutions (y vs. x) and (y vs. x) in a and b on the same graph and make your comments on the behavior of the system, accuracy and stability.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q5: Given the following coupled system of ODES ý, = 988y -1998y, Ý, = 1000y,-2000yz with y; (0)= 1, y:(0)=2 a) Solve the system using Explicit Euler with h= 0.00001, 0.001 and 0.01 for 0x0.5. b) Solve the system using Implicit Euler with h= 0.00001, 0.001 and 0.01 for 0x0.5. c) Plot the solutions (y vs. x) and (y vs. x) in a and b on the same graph and make your comments on the behavior of the system, accuracy and stability.
Transcribed Image Text:Q5: Given the following coupled system of ODES ý, = 988y -1998y, Ý, = 1000y,-2000yz with y; (0)= 1, y:(0)=2 a) Solve the system using Explicit Euler with h= 0.00001, 0.001 and 0.01 for 0x0.5. b) Solve the system using Implicit Euler with h= 0.00001, 0.001 and 0.01 for 0x0.5. c) Plot the solutions (y vs. x) and (y vs. x) in a and b on the same graph and make your comments on the behavior of the system, accuracy and stability.
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